The present invention relates to a method of processing an image in an X-ray diagnosing device used in medical treatment or in non-destructive examination of objects used in industries industrial applications.
FIG. 6 illustrates attenuation of X-rays resulting from the X-rays being transmitted through objects. The intensities of the X-rays I.sub.1 (E) transmitted through objects (1)1 and (2)2 having a thickness of d.sub.1 and d.sub.2, respectively, are given by EQU I.sub.1 (E)=I.phi.(E) exp {-.mu..sub.A (E)d.sub.1 -.mu..sub.B (E)d.sub.2 }(1)
where I.sub.0 (E) is the intensity of the X-rays output from an X-ray tube 3, and .mu..sub.A (E) and .mu..sub.B (E) are the attenuation coefficients of the objects (1)1, (2)2, respectively.
If the energy E of the X-rays is divided into two zones Low and High, and both sides of each of those zones, are converted logarithmically the following is obtained: EQU -lnI'(Low)=.mu..sub.A (Low)d.sub.1 +.mu..sub.B (Low)d.sub.2( 2) EQU -lnI'(High)=.mu..sub.A (High)d.sub.1 +.mu..sub.B (High)d.sub.2( 3) EQU I'(Low)=I(Low)/I.phi.(Low) EQU I'(High)=I(High)/I.phi.(High)
Rewriting equation (2) and (3), using -lnI'(Low)=S(Low) and -lnI'(High)=S(High), obtained EQU S(Low)=.mu..sub.A (Low)d.sub.1 +.mu..sub.B (Low)d.sub.2 ( 4) EQU S(High)=.mu..sub.A (High)d.sub.1 +.mu..sub.B (High)d.sub.2 ( 5)
Solving equations (4) and (5) with respect to d.sub.1 and d.sub.2, obtained EQU d.sub.1 =1/.DELTA.x{.mu..sub.B (High)S(Low)-.mu..sub.B (Low)S(High)}(6) EQU d.sub.2 =1/.DELTA.x{-.mu..sub.A (High)S(Low)+.mu..sub.A (Low)S(High)}(7)
The attenuation coefficients are values inherent to the materials of the objects. Thus if equations (6) and (7) are rewritten as functions of S(Low) and S(High) using coefficients a.sub.1 -a.sub.4, then the following is obtained EQU d.sub.1 =a.sub.1 S(Low)+a.sub.2 S(High) (8) EQU d.sub.2 =a.sub.3 S(Low)+a.sub.4 S(High) (9)
Equations (8) and (9) will be described using an X-ray transmission picture. Only picture components corresponding to the thickness of a specific object can be extracted from the X-ray transmission picture as a linear function of a logarithmic conversion version of the X-ray transmission picture. This method is illustrated in the following reference as energy subtraction method (differential method):
Ishida, "Hardware and Software for Picture Processing", Japanese Journal of Medical Electronics and Biological Engineering Vol. 22, No. 1, P. 53. PA1 a.sub.1 =1 PA1 a.sub.2 =-1.13 PA1 using a semiconductor radiation detector; PA1 providing two discriminating levels; PA1 dividing X-rays, which have passed through objects, into two kind energy band; PA1 counting X-ray photons to obtain an x-ray picture; PA1 assembling, with corresponding coefficients, S(H), S(L), {S(H)}.sup.x and {S(L)}.sup.y, which are exponential functions of the S(H) and S(L), respectively, where S(H) is a logarithmically converted version of a picture of counts in a higher energy band and S(L) is a logarithmically converted version of a picture of counts in a lower energy band; and PA1 performing addition, subtraction, multiplication and/or division on these terms to provide a picture in which a particular one of the materials constituting the objects is selectively extracted or removed.
The above method will now be described in a practical field. As an example, assume that the objects (1) and (2) are aluminum and water, respectively. FIG. 7 illustrates the linear attenuation coefficients .mu. of aluminum and water. As will be seen in FIG. 7, the respective coefficients are non-linear as a function of the X-ray energy, and rapidly increase toward the lower-energy side, which increase influences the X-ray spectrum, as shown in FIG. 8. In FIG. 8, the axis of ordinates indicates the X-ray photons, the curve (1) indicates the X-ray spectrum emitted from a regular source of X-rays at a tube voltage of 120 KV.sub.p and the curves (2) and (3) indicate changes in the X-ray spectra transmitted through objects when the thickness of the object increases. As will be understood in FIG. 8, as the thickness of the object increases, the object absorbs more of the lower energy X-rays and the average energy of the transmitted X-ray spectrum shifts toward the higher energy side, which is referred to as beam-hardening.
Energy subtraction, illustrated in equations (8) and (9) in a field where such beam hardening occurs, will be applied in actual irradiation. FIG. 9 shows the shape of objects (1) and (2) used in experiments where the objects (1) and (2) are an aluminum strip 0.5 cm thick and a water body 20 cm high and shows the direction of X-ray irradiation incident on the objects. Such objects were irradiated with X-rays at an X-ray tube voltage of 120 KV.sub.p and a semiconductor radiation detector was used to scan the objects to thereby obtain transmitted pictures. The signals from the detector are separated with discriminating levels at 20 and 60 KeV. The logarithmic converted values of picture signals in 20-60 KeV and in 60-120 KeV are represented by S(Low) and S(High), respectively. The value of coefficient a was determined such that a picture of aluminum alone, namely, a picture where a water picture is erased, is obtained. The values of a.sub.1 and a.sub.2 used to obtain the aluminum d.sub.1 picture using equation (8) are as follows:
FIG. 10 shows the remainder of the water signal component contained in the waterless picture and an aluminum picture signal component with the thickness of water, obtained in that case. If water is erased at a water thickness of 10 cm, the water signal component is null at that water thickness. The thickness of water increases or otherwise decreases, the remaining water signal component will be contained in the resulting picture. This is noticeable especially when the water is thin. The aluminum component has a uniform contrast difference obtained as the difference between the aluminum component and remaining water components all over the cross-section region of water. This is illustrated as an actual picture in FIG. 11 in which a water picture disappeared completely from the image screen in the vicinity of a water thickness of 10 cm and the aluminum picture alone is extracted. In a region where the water thickness is smaller or otherwise larger, the remaining water picture component appears.
As described above, the energy subtraction method cannot make an ideal subtraction over the entire cross-section regions of the objects if the thickness of the objects changes using the difference of lograithmic conversion pictures alone, as in the converting techniques.